One of the main challenges in high-frequency finance is the irregular arrival of prices. Once you get down to the tick by tick prices, you can't count on normal interval time series. There are autoregressive models which support irregular arrival of prices. Engle and Russell's autoregressive conditional duration (ACD) model comes to mind (described in Econometric Modeling of Multivariate Irregularly-Spaced High-Frequency Data which extends the Engle-Russell Autoregressive Conditional Duration (ACD) model for the multivariate case).
Taking a sampling of SPY data from my broker shows a mean time between last trade of 2.1s with a standard deviation of 2.4s. The minimum time elapsed between "ticks" (really consolidated market data messages) appears to be 250ms, potentially several trade lifecycles in high frequency land. The median time between last "ticks" is 1.0s. At one level, this should not be surprising. I am seeing ~97ms and ~161ms latency due to international data feeds. The theoretical contribution due to propagation delay (2/3 c) is about 19.9ms and 36.5ms. Most of my problem is my connection, but at least part of it is due to the non-direct route of the backbone fiber linking major market centers. This is why some shops and vendors are looking into wireless connections between Chicago and New York. Roughly 7ms of the former and 10ms of the latter may be attributable to connection specific issues. Moving my location closer to one data center reduces the latency down to 48ms but increases latency to the other to 192ms. Getting right in the same town as the market data server gets us to 2.25ms.
Concerning the characteristics of the data, the SPY data does appear to be somewhat higher frequency than the ES data (2.2s from my last post). This is of course to be expected. What betrays the performance issue is the fact that the difference between SPY and ES data should be even greater given the far greater volume for SPY.My previous post on trade frequency looked at frequency data for the S&P E-mini contract ES.